Results 31 to 40 of about 1,964,264 (277)
Visualization of Mandelbrot and Julia Sets of Möbius Transformations
Fractal and Fractional, 2021 This work reports on a study of the Mandelbrot set and Julia set for a generalization of the well-explored function η(z)=z2+λ. The generalization consists of composing with a fixed Möbius transformation at each iteration step.
Leah K. Mork, Darin J. Ulness
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Quasisymmetrically inequivalent hyperbolic Julia sets [PDF]
, 2012 We give explicit examples of pairs of Julia sets of hyperbolic rational maps which are homeomorphic but not quasisymmetrically ...
Pilgrim, Kevin, Haïssinsky, Peter
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Filled Julia Sets of Chebyshev Polynomials [PDF]
, 2021 We study the possible Hausdorff limits of the Julia sets and filled Julia sets of subsequences of the sequence of dual Chebyshev polynomials of a non-polar compact set K⊂ C and compare such limits to K.
Christiansen, Jacob Stordal +13 more
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Boundaries of Filled Julia Sets in Generalized Jungck Mann Orbit
IEEE Access, 2019 In this paper, we study the generalized Jungck Mann orbit (GJMO) and prove the converse theorem of results. We develop algorithms for the generation of filled Julia sets and their boundaries in the GJMO.
Dong Li +3 more
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Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices
Discrete Dynamics in Nature and Society, 2020 The fractional Potts model on diamond-like hierarchical lattices is introduced in this manuscript, which is a fractional rational system in the complex plane. Then, the fractal dynamics of this model is discussed from the fractal viewpoint.
Weihua Sun, Shutang Liu
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Control and synchronization of Julia sets of the complex dissipative standard system
Nonlinear Analysis, 2016 The fractal behaviors of the complex dissipative standard system are discussed in this paper. By using the boundedness of the forward and backward orbits, Julia set of the system is introduced and visualization of Julia set is also given.
Weihua Sun, Yongping Zhang
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Fractal and Fractional, 2021 In this paper, a novel escape-time algorithm is proposed to calculate the connectivity’s degree of Julia sets generated from polynomial maps. The proposed algorithm contains both quantitative analysis and visual display to measure the connectivity of ...
Yang Zhao +3 more
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Hypercomplex iterations-distance estimation for generalized Julia and Mandelbrot sets.
, 1997 Hypercomplex iterations-distance estimation for generalized Julia and Mandelbrot ...
Yumei. Dang (7984745)
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Fractal Generation in Modified Jungck–S Orbit
IEEE Access, 2019 The aim of this paper is to modify the Jungck-S iterative scheme by adding the idea of s-convexity. We define and analyze the modified Jungck-S orbit (MJSO) with s-convex combination and derive the escape criterion for MJSO.
Young Chel Kwun +4 more
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Julia sets and differential equations [PDF]
Proceedings of the American Mathematical Society, 1993 Summary: A one-parameter family of Julia sets is shown to converge, in a probabilistic sense, to certain trajectories of a differential equation. The Julia sets arise from Euler's method for the differential equation. This provides information on the location of the Julia sets and the dynamics on them.
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